Decision Trees

Posted on May 15 2009

Decision trees are a chronological and hierarchical representation of the decision process. It utilizes a combination of two types of nodes: decision (choice) nodes (usually represented by a square ), and states of nature (chance) nodes (usually represented by circles).

They are used when a combination of choices based on each result is selected as a decision alternative. A person trained in information technology might recognize the tree as an “if-then-else” approach.

Building the Tree

Construct the tree utilizing the logic of the problem. For the chance nodes, ensure that the probabilities along any outgoing branch sum to one. Calculate the expected payoffs by rolling the tree backward (i.e., starting at the right and working toward the left).

You may imagine driving your car; starting at the foot of the decision tree and moving to the right along the branches. At each square you have control, to make a decision and then turn the wheel of your car. At each circle, Murphy takes over the wheel and you are powerless.

Step-By-Step

Here is a step-by-step description of how to build one:

1. Draw the tree using squares to represent decisions and circles to represent uncertainty,

2. Evaluate the tree to make sure all possible outcomes are included,

3. Calculate the tree values working from the right side back to the left,

4. Calculate the values of uncertain outcome nodes by multiplying the value of the outcomes by their probability

On the tree, the value of a node can be calculated when we have the values for all the nodes following it. The value for a choice node is the largest value of all nodes immediately following it. The value of a chance node is the expected value of the nodes following that node, using the probability of the arcs.

By rolling the tree backward, from its branches toward its root, you can compute the value of all nodes including the root of the tree. Putting these numerical results in a graph.

Once a decision trees has been selected as the choice alternative, and the decision is made, the tree can be used to document the decision.

See more information on Decision Making Tools or check out our DECIDE GUIDES for Decision Guides which utilize the decision tree and other tools and processes